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A Notion Of Rectifiability Modeled On Carnot Groups, Scott D. Pauls
A Notion Of Rectifiability Modeled On Carnot Groups, Scott D. Pauls
Dartmouth Scholarship
We introduce a notion of rectifiability modeled on Carnot groups. Precisely, we say that a subset E of a Carnot group M and N is a subgroup of M, we say E is N-rectifiable if it is the Lipschitz image of a positive measure subset of N. First, we discuss the implications of N-rectifiability, where N is a Carnot group (not merely a subgroup of a Carnot group), which include N-approximability and the existence of approximate tangent cones isometric to N almost everywhere in E. Second, we prove that, under a stronger condition concerning the existence of approximate tangent cones …
Two New Criteria For Comparison In The Bruhat Order, Brian Drake, Sean Gerrish, Mark Skandera
Two New Criteria For Comparison In The Bruhat Order, Brian Drake, Sean Gerrish, Mark Skandera
Dartmouth Scholarship
We give two new criteria by which pairs of permutations may be compared in defining the Bruhat order (of type $A$). One criterion utilizes totally nonnegative polynomials and the other utilizes Schur functions.
Computing Isotypic Projections With The Lanczos Iteration, David K. Maslen, Michael E. Orrison, Daniel N. Rockmore
Computing Isotypic Projections With The Lanczos Iteration, David K. Maslen, Michael E. Orrison, Daniel N. Rockmore
Dartmouth Scholarship
When the isotypic subspaces of a representation are viewed as the eigenspaces of a symmetric linear transformation, isotypic projections may be achieved as eigenspace projections and computed using the Lanczos iteration. In this paper, we show how this approach gives rise to an efficient isotypic projection method for permutation representations of distance transitive graphs and the symmetric group.